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The Central Limit Theorem

The Central Limit Theorem explains that the greater the sample size for a random variable, the more the sampling distribution of the sample means approximate a normal distribution.

 

Discrete distributions become normally distributed

 

Sampling distributions of sample means deriving from any probability distribution (even discrete probability distributions) become normally distributed, when the sample size is sufficiently large and the sample mean and sample standard deviation are well defined.

 

 

The Central Limit Theorem is fundamental in statistics

 

The Central Limit Theorem is fundamental in statistics and one of the most profound concepts when dealing with probability distribution and mathematics. It explains why the normal distribution is a central distribution in real-life data.

So, for any probability distribution, the greater the sample size the more the sampling distribution of the sample mean, approximates to the normal distribution:

 

 central limit theorem

 

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